The ultimate goal of this research is to produce PDESYS, a software package for personal computers which provides an interactive graphical environment for defining, solving and viewing the solutions to systems of parabolic and elliptic partial differential equations (pde's) on arbitrary 1- and 2- dimensional spatial domains. The finite element method will be used to solve these equations on 2-dimensional domains. For 1-dimensional domains, both finite element and finite difference methods will be available. Pde's of the type to be handled by the proposed PDESYS software are ubiquitous in biomedicine, science, and engineering. Heart transfer, electro-diffusion, reaction-diffusion, nerve-impulse transmission, capillary/tissue exchange, and macro-molecular percolation in tissue are only a few of the many areas in which these equations arise. Existing packages for solving pde's are large and difficult to use, and none of them is available for microcomputers. These packages are efficient only on special problems and provide unfriendly user interfaces. We intend to design a system which will be convenient, flexible, and efficient. It will be suitable for users who are less technically proficient in numerical analysis. What will distinguish this package from others is that, when there is a tradeoff between convenience and efficiency, we will tilt toward convenience. PDESYS will use the MLAB modeling language as its interactive graphical shell.